I grew up in Manila and now live in LA. If you have 2-3 weeks, I would spend maybe a week at most in Manila to explore the city and get over jet lag, then definitely go to Boracay and Palawan the rest of the time to relax.

In Manila, people usually like the BGC/Makati area to stay. Explore the malls (Megamall, Mall of Asia, etc.), go to Intramuros, visit old churches, maybe go to old Manila area like Quiapo/Chinatown/Escolta. Recommend doing a day trip to Tagaytay.